I don't believe so.
See, crossbreeding between animals and aliens would be a hybridization, and we have a lot of barriers against hybridization. Reproduction itself is a process with a lot of controlling systems.
We have prezygotic barriers, which are the barriers that prevent two different species to crossbreed. That could be: too different body shapes, or behaviours, flowering in different seasons, occurring in different places (isolated from each other), lack of chemical recognition between ovule and sperm, too different genomes....
And we also have postzygotic barriers, which would prevent the development of an zygote even if these different species mate. That could be poor development or abortion of the hybrid zygote, sterility of this hybrid...
Thus, your aliens would have to deal with all these controlling systems... They would need to have chromosomes similar enough to ours for chromosome pairing... or a system that could mislead and deceive this very important and central issue in reproduction, which is genetic compatibility.
It's important to note that hybridization does occur in nature and is a very important phenomena in evolution dynamics, but a lot of conditions are to be satisfied for that, and a certain compatibility must exist. Take a moment to look into this very nice paper: Hybridization as an invasion of the genome. It has a section named Factors affecting the frequency of hybridization that will enlight you about some controlling mechanisms.
The nice thing is:
You know there is a theory according to which life could have gotten here from space, right? That's Panspermia Theory.
You can read more about that here:
A mechanism for interstellar panspermia
Comets-a vehicle for panspermia
If life was travelling trough space, in order to evolve here and in other planet in a way terrestrial and alien species would have the same DNA structure based life, both planets would have to have the same conditions for species to evolve under. Even if they did, the mechanisms that prevent two terrestrial species to crossbreed would certainly work for two species from different planets.
But the advantage is, this is worldbuilding, right?
Given that the universe is infinite, who knows if there aren't such similar planets over there? Also, alien technologies could recreate, simulate, incorporate terrestrial structures... I don't know... you can use your imagination... They can study terrestrial structures and learn how to manipulate genes to express and recreate morphological characteristics they have out there, and then use DNA as their own structures...
And if they do so.. scientific literature is full of examples of hybridization as a form of species invasion (respected the compatibilities)
For example, hybrids can be less adapted and die... but they also can have the best of each species they came from, and them be able to coup better with more extreme conditions and outcompete their parentals. A world of possibilities lies there. If you get interested, let me know, I can give you a lot of scientific literature (as it is my work)
Mallet, J. (2005). Hybridization as an invasion of the genome. Trends in ecology & evolution, 20(5), 229-237.
Napier, W. M. "A mechanism for interstellar panspermia." Monthly Notices of the Royal Astronomical Society 348.1 (2004): 46-51.
Burchell, Mark J. "Panspermia today." International Journal of Astrobiology 3.2 (2004): 73-80.
Hoyle, Fred, and Chandra Wickramasinghe. "Comets-a vehicle for panspermia." Comets and the Origin of Life. Springer Netherlands, 1981. 227-239.